How to scale along the local axis of an object?
When you are in edit mode, select the desired vertices, press S, and then press either X, Y, or Z twice in a row. 

After the first press it will transform along the global orientation as usual:



After the second press it will use the transform orientation selected in 3D view > header, which is set to local by default:



If the orientation is set to global pressing the axis key (X,Y,Z) twice will still use the corresponding local axis.

This solution does not work if the vertices were rotated in edit mode. For that you may have to change the transform orientation to normal, and manually move the edges.